The probabilities of a problem being solved b | vedclass

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(A) Let $A$ and $B$ be the events that the problem is solved by the first and second student,respectively.Given $P(A) = \frac{1}{2}$ and $P(B) = \frac

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$\frac{2}{3}$

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(A) Let $A$ and $B$ be the events that the problem is solved by the first and second student,respectively.Given $P(A) = \frac{1}{2}$ and $P(B) = \frac{1}{3}$.The probability that the problem is not solved by either student is $P(A^c \cap B^c) = P(A^c) 	imes P(B^c)$.$P(A^c) = 1 - \frac{1}{2} = \frac{1}{2}$.$P(B^c) = 1 - \frac{1}{3} = \frac{2}{3}$.So,$P(A^c \cap B^c) = \frac{1}{2} 	imes \frac{2}{3} = \frac{1}{3}$.The probability that the problem is solved is $P(A \cup B) = 1 - P(A^c \cap B^c) = 1 - \frac{1}{3} = \frac{2}{3}$.

The probabilities of a problem being solved by two students are $\frac{1}{2}$ and $\frac{1}{3}$. Then the probability of the problem being solved is

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